Simple Velocity question

Hi ritwik

The average speed over the time of a complete cycle? I think you made a mistake. Look at the sin function again and think of it's average value. It can be done without integrating or any calculus whatsoever. Or am I wrong?

 

Hi ritwik06,

Your result looks right to me.

 

ritwik, your result is wrong.
what limits did you take for integrating?

 

Well, I only wanted to help and solve the problem in the process. So were is no reason to laugh at me

I just thought that if velocity varies from u to -u then the average value will be just zero. Of course if we are talking about the absolute value of u then [tex] \frac{2u}{\pi} [/tex] is the answer

Sorry, I didn't mean that

 

Hi jablonsky27,

I got the same answer as ritwik. Are you integrating the correct function (they ask for the average speed)?

 

hi alphysicist,
you dont even have to integrate the given function. the average value of a sine(or cosine) over one cycle is always zero. the velocity function mentioned, is a sine with no additional constant term. so its average value too over one cycle will be zero.
if, you really want to calculate it,


Vaverage = (1/T).[tex]\int[/tex](u.sinwt) over the limits 0 to T,

= (u/T).[-cos(w.2/[tex]\Pi[/tex]T) + cos(0)]

= (u/T).[-1 + 1]

= 0

hopefully, it makes sense. first time with Latex.

 

jablonsky,

I see ritwik already remarked about how we are looking for the average speed (not average velocity). So the integral to calculate would be:




[tex]
\mbox{average speed }= \frac{1}{T}\ \int\limits_0^Tdt\ |u \sin(\omega t)|
[/tex]

Or you could restrict the integral to just one-fourth of a period.

 

oh ya. sorry. should learn to read questions more carefully in the future.